Anna Frascella

Fuzzy Galois connections under weak conditions

Operators that allow to transport L-sets along binary L-relations are considered, assuming L to be a quite general lattice-ordered algebra. Functoriality conditions and fuzzy Galois connections involving these operators, already known for a complete residuated lattice L, are investigated in case of complete distributive extended-order algebras that need not be commutative or associative.

Transporting many-valued sets along many-valued relations

The transport of L-sets along an L-relation R is considered, with L any residuated lattice, sometimes with further properties as to be a frame or an MV-algebra. Pairs of powerset operators related to R are considered and their basic properties are studied in a comprehensive discussion including some results already known. A few examples and suggestions for application and further development are also given.

Structured lattices and ground categories of L-sets

Complete lattices are considered with suitable families of lattice morphisms that provide a structure ( L , Φ ) , useful to characterize ground categories of L -sets by means of powerset operators associated to morphisms of these categories. The construction of ground categories and powerset operators presented here extends and unifies most approaches previously considered, allowing the use of noncrisp objects and, with some restriction, the change of base. A sufficiently large category of L -sets that includes all possible ground categories on a structured lattice ( L , Φ ) is provided and studied, and its usefulness is justified. Many explanatory examples have been given and connection with the categories considered by J. A. Goguen and by S. E. Rodabaugh are stated.